The integral formula of the volume rotating around the X axis is V=π∫[a, b] f (x) 2dx. Similarly, the formula for rotating the volume around the Y axis can be interchanged with X and Y, V = π∫ [a, b] φ (y) 2dy; Or V=2π∫[a, b]y*f(y)dy, which is also the volume rotating around the X axis; The lateral area of an object rotating around the X axis is A=2π∫[a, b] y * (1+y' 2) 0.5dx, where y' 2 is the square of the derivative of y to X.

Definite integral narration

Definite integral and indefinite integral seem to have nothing to do, but they are closely related in essence because of the support of a mathematically important theory. It seems impossible to subdivide a graph infinitely and then accumulate it, but because of this theory, it can be transformed into calculating integral.

It is precisely because of this theory that the relationship between integral and Riemann integral is revealed, which shows its important position in calculus and even higher mathematics. Therefore, Newton-Leibniz formula is also called the basic theorem of calculus.